12x^2+16x^2=10^2

Solution for 12x^2+16x^2=10^2 equation:

12x^2+16x^2=10^2

We move all terms to the left:

12x^2+16x^2-(10^2)=0

We add all the numbers together, and all the variables

28x^2-100=0

a = 28; b = 0; c = -100;
Δ = b2-4ac
Δ = 02-4·28·(-100)
Δ = 11200
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{11200}=\sqrt{1600*7}=\sqrt{1600}*\sqrt{7}=40\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-40\sqrt{7}}{2*28}=\frac{0-40\sqrt{7}}{56}
=-\frac{40\sqrt{7}}{56}
=-\frac{5\sqrt{7}}{7}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+40\sqrt{7}}{2*28}=\frac{0+40\sqrt{7}}{56}
=\frac{40\sqrt{7}}{56}
=\frac{5\sqrt{7}}{7}
$